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An Improved Divide-and-Conquer Algorithm for Finding All Minimum k-Way Cuts

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Algorithms and Computation (ISAAC 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5369))

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Abstract

Given a positive integer k and an edge-weighted undirected graph G = (V,E;w), the minimum k -way cut problem is to find a subset of edges of minimum total weight whose removal separates the graph into k connected components. This problem is a natural generalization of the classical minimum cut problem and has been well-studied in the literature.

A simple and natural method to solve the minimum k-way cut problem is the divide-and-conquer method: getting a minimum k-way cut by properly separating the graph into two small graphs and then finding minimum k′-way cut and k′′-way cut respectively in the two small graphs, where k′ + k′′ = k. In this paper, we present the first algorithm for the tight case of \(k'=\lfloor k/2\rfloor\). Our algorithm runs in \(O(n^{4k-\lg k})\) time and can enumerate all minimum k-way cuts, which improves all the previously known divide-and-conquer algorithms for this problem.

The work was done when the author was a PhD student in Department of Computer Science and Engineering, the Chinese University of Hong Kong.

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Authors and Affiliations

  1. School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu, 610054, China

    Mingyu Xiao

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  1. Mingyu Xiao
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Editor information

Editors and Affiliations

  1. School of Information Technologies, University of Sydney, Australia

    Seok-Hee Hong

  2. Graduate School of Informatics, Kyoto University, 606-8501, Kyoto, Japan

    Hiroshi Nagamochi

  3. Graduate School of Informatics, Kyoto University, Japan

    Takuro Fukunaga

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Xiao, M. (2008). An Improved Divide-and-Conquer Algorithm for Finding All Minimum k-Way Cuts. In: Hong, SH., Nagamochi, H., Fukunaga, T. (eds) Algorithms and Computation. ISAAC 2008. Lecture Notes in Computer Science, vol 5369. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-92182-0_21

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  • DOI: https://doi.org/10.1007/978-3-540-92182-0_21

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-92181-3

  • Online ISBN: 978-3-540-92182-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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